Implicit differentiation

Implicit differentiation

So far, we have always tried to configure a relation to an explicit function in the form of y = f(x) before finding the derivative of the relation, but what if this is impossible to do so? In this section, we will first learn to identify the difference between explicit functions and implicit functions. Then we will learn how to differentiate a relation with a mix of variables x and y using the method called Implicit Differentiation.

Lessons

Introduction

Explicit Functions VS. Implicit Functions

1.

The graph shows a circle centred at the origin
with a radius of 5.

a) Define the circle implicitly by a relation
between x and y .
b) Define the circle by expressing y explicitly
in terms of x .
c) Use the method of "explicit differentiation" to find the
slope of the tangent line to the circle at the point (4, -3).
d) Use the method of "implicit differentiation" to find the
slope of the tangent line to the circle at the point (4, -3).